Exotic option pricing in Heston's stochastic volatility model:
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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2008
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 143 S. graph. Darst. |
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| 245 | 1 | 0 | |a Exotic option pricing in Heston's stochastic volatility model |c von Susanne A. Griebsch |
| 264 | 1 | |c 2008 | |
| 300 | |a XI, 143 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 502 | |a Frankfurt am Main, School of Finance & Management, Diss., 2008 | ||
| 650 | 7 | |a Optionsgeschäft |2 stw | |
| 650 | 7 | |a Optionspreistheorie |2 stw | |
| 650 | 7 | |a Stochastischer Prozess |2 stw | |
| 650 | 7 | |a Theorie |2 stw | |
| 650 | 7 | |a Volatilität |2 stw | |
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Datensatz im Suchindex
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| adam_text | Titel: Exotic option pricing in Heston s stochastic volatility model
Autor: Griebsch, Susanne
Jahr: 2008
Contents
Preface 1
1 Heston s Stochastic Volatility Model 5
1.1 Introduction........................................ 5
1.2 Option Pricing in the Heston Model.......................... 6
1.2.1 Partial Differential Equation for a Contingent Claim............. 6
1.2.2 Risk-neutral Pricing with respect to A..................... 8
1.2.3 Numerical Pricing Methods versus (Semi-) Analytical Pricing Formulas . 10
2 Numerical Simulation Methods 15
2.1 Exact Simulation Scheme................................. 15
2.2 Monte Carlo Methods .................................. 17
2.2.1 Euler Scheme and Remedies .......................... 18
2.2.2 Higher Order Discretization Scheme...................... 20
2.2.3 Andersen Scheme................................. 20
2.3 Complex Logarithm Problem and Numerical Integration.............. 22
3 FX Market Data Situations 26
3.1 Calibration of Heston s Model to FX Market Data .................. 26
3.2 How to Price Exotic Options in the Heston Model?.................. 28
4 Characteristic Functions 34
4.1 Derivation of the ra-variate Characteristic Functions................. 34
4.2 Moment Stability..................................... 40
4.3 Applications of Characteristic Functions in Option Pricing............. 42
5 Fader Options 45
5.1 Introduction to Fader Options.............................. 45
5.2 Pricing of Fader Options in the Heston Model .................... 46
Contents
6 Numerical Results for Fader Options 49
7 Discretely Monitored Barrier Options 51
7.1 Introduction to Discrete Barrier Options........................
7.2 Pricing of Discrete Barrier Options in the Heston Model............... 53
8 Computational Issues for Discrete Barrier Options 57
8.1 Implementational Aspects of the Fast Fourier Transform Method ......... 57
8.2 Discussion of Numerical Results............................
8.2.1 Comparison of Accuracy and Computational Time............. 60
8.2.2 Continuity Correction.............................. 65
9 Affine (Jump) Diffusion Stochastic Volatility Models 69
9.1 Affine Diffusion Models................................. 70
9.2 Affine Jump Diffusion Models.............................. 72
9.3 Multidimensional Heston Models............................ 74
9.4 A Characterization.................................... 79
10 Compound Options 80
10.1 Introduction to Compound Options.......................... **°
10.2 Pricing of Compound Options in the Heston Model................. ^2
10.2.1 Characteristic Function Approach....................... °2
10.2.2 Transition Density Approach.......................... ^
10.2.3 Mixed Method Approach............................ 85
11 Numerical Pricing Algorithm for Compound Options 87
11.1 Basic Approach...................................... 87
11.2 Application of the FFT Algorithm............................ 92
11.3 Digression......................................... 93
11.4 Further Development of the Algorithm ........................ 96
11.5 The Compound(ed) Algorithm.............................102
12 Concluding Remarks 106
Appendix 109
A Put-Call Symmetry for Barrier Options 110
B Derivation of the Bivariate Characteristic Function 112
C The Sch bel Zhu, Bates and Multifactor Heston Model 11s
C.1 Sch bel ZhuModel.............. . . 115
Contents
C.2 The Bates and SVCJ Model................................116
C.3 The Two-Dimensional Heston Model..........................117
C.4 The Multifactor Heston Model .............................118
D Calculations for the Compound Option Pricing Algorithm 121
D.I Characteristic Functions.................................121
D.2 Solving the Fourier Inversion..............................122
E Selected Pieces of Source Code 124
E.I Mathematica Programs..................................124
E.2 C# Programs........................................126
E.3 R Programs ........................................131
F Tools 133
F.I Exponential Martingale..................................133
F.2 The Spot Measure and its Numeraire..........................134
F.3 Correlation.........................................135
Bibliography 137
List of Symbols 141
List of Tables
2.1 Euler discretization schemes in the Heston model...................
3.1 Parameters in Heston s model fitted to one years volatility smiles.......... 29
3.2 At-the-money vanilla call values ............................ 30
3.3 Fader values based on the model parameters of three examples .......... 3:2
3.4 Analytic fader values based on the model parameters of three examples..... 32
6.1 Parameter settings for fader option pricing...................... ^
6.2 Numerical results for fader call option values in the Heston model........ 50
7.1 Impact of the monitoring frequency on the value of a down-and-out barrier call
option............................................ 53
8.1 Example set of model parameters for the pricing of discrete barrier options . . • 61
8.2 Down-and-out discrete barrier option values in the Heston model.........
8.3 Up-and-out discrete barrier option values in the Heston model........... 64
8.4 Continuous versus discrete down-and-out call in the Heston model - the barrier
shift method........................................ 66
8.5 Continuous versus discrete down-and-out call in the Heston model - the Black-
Scholes adjustment method............................... 67
8.6 Continuous versus discrete down-and-out call in the Heston model - the extrap-
olation method..................................... 68
List of Figures
3.1 Implied volatility in Heston s model fitted to one year volatility smiles....... 29
3.2 Comparison of variance and spot sample paths.................... 33
5.1 Sample path for a fader option ............................. 46
7.1 Sample paths for a discretely monitored barrier knock-out option.......... 54
8.1 Barrier shift in the Black-Scholes model compared to the Heston model...... 68
10.1 Lifetime of mother and daughter option for compound options........... 81
11.1 Exercise region for a compound option in the Heston model............ 89
11.2 Concept of the approximation of compound option values in the Heston model . 90
11.3 Numerical comparison of U(ui,v) and Jr^1{ipXtV(ui,u1)).............. 97
11.4 Fourier inversion before and after the application of the Laplace inversion .... 100
11.5 Fourier inversion shifted by its corresponding residues............... 102
11.6 Differences of the function at the beginning and at the end of the calculations . . 103
11.7 Exercise region of a compound option......................... 104
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| id | DE-604.BV035908549 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:07:11Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018765858 |
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| physical | XI, 143 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| spelling | Griebsch, Susanne Verfasser (DE-588)133576108 aut Exotic option pricing in Heston's stochastic volatility model von Susanne A. Griebsch 2008 XI, 143 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Frankfurt am Main, School of Finance & Management, Diss., 2008 Optionsgeschäft stw Optionspreistheorie stw Stochastischer Prozess stw Theorie stw Volatilität stw Optionspreistheorie (DE-588)4135346-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Optionspreistheorie (DE-588)4135346-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018765858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Griebsch, Susanne Exotic option pricing in Heston's stochastic volatility model Optionsgeschäft stw Optionspreistheorie stw Stochastischer Prozess stw Theorie stw Volatilität stw Optionspreistheorie (DE-588)4135346-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4135346-8 (DE-588)4114528-8 (DE-588)4113937-9 |
| title | Exotic option pricing in Heston's stochastic volatility model |
| title_auth | Exotic option pricing in Heston's stochastic volatility model |
| title_exact_search | Exotic option pricing in Heston's stochastic volatility model |
| title_full | Exotic option pricing in Heston's stochastic volatility model von Susanne A. Griebsch |
| title_fullStr | Exotic option pricing in Heston's stochastic volatility model von Susanne A. Griebsch |
| title_full_unstemmed | Exotic option pricing in Heston's stochastic volatility model von Susanne A. Griebsch |
| title_short | Exotic option pricing in Heston's stochastic volatility model |
| title_sort | exotic option pricing in heston s stochastic volatility model |
| topic | Optionsgeschäft stw Optionspreistheorie stw Stochastischer Prozess stw Theorie stw Volatilität stw Optionspreistheorie (DE-588)4135346-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Optionsgeschäft Optionspreistheorie Stochastischer Prozess Theorie Volatilität Mathematisches Modell Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018765858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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